Estimation of the 
norm using an SDP
Update: This is utter bollocks, but I’ve yet to get around to correcting it.
Continuing in the vein of the previous post, we have that 
, so if we’re interested in approximating 
(which looks like it’s hard to compute exactly), then we’d find it useful to be able to compute 
. It turns out this is easily done with an SDP when 
is strictly positive:
Then 
. I’m not sure what happens if 
isn’t full rank, and this definitely won’t work if is not positive semi-definite.
Possibly relevant posts:
- Trace dual of the
norm (1/19/2010) - Dual of an inequality and equality constrained SDP (2/26/2010)
- A failed attempt to use an SDP to find a nonorthogonal factorization (1/17/2010)
norm